This project investigates two fundamental problems in biology: (1) the kinetics of enzymes located in cell membranes, and (2) thermodynamics of bioenergetic mechanisms in mitochondria. Mathematical analysis, simulation on digital computers, and numerical solution of nonlinear algebraic and differential equations are the main tools in these investigations. While these problems are diverse in their biological background, they all share in a common basis of mathematical and physical content in the role played by conservation laws and in the mathematical methods involved in their resolution.